Embedding partial G-designs where G is a 4-cycle with a pendant edge

Abstract

Let D denote the graph consisting of a cycle of length 4 with a pendant edge. In this paper, two very different small embeddings of partial D-designs are presented.

Tight embeddings of partial quadrilateral packings

“…The case Λ(n; D) where D denotes the five-vertex graph consisting of a 4-cycle with a pendant edge attached was studied by Jenkins [10], he showed Λ(n; D) 4n + 22.…”

Completing partial packings of bipartite graphs

“…Many bounds of the type, f (n; H) ≤ c(H)n have been proved for various graphs H by explicit constructions. A (by no means complete) list of references includes Hoffman, Küçükçifçi, Lindner, Roger, Stinson [8], [10], [11], [12], [13], [14], Jenkins [9], Bryant, Khodkar and El-Zanati [3]. See also Füredi and Lehel [4] for a survey of their results.…”